TURBOMOLE is a collaborative, multi-national software development project aiming to provide highly efficient and stable computational tools for quantum chemical simulations of molecules, clusters, periodic systems, and solutions. The TURBOMOLE software suite is optimized for widely available, inexpensive, and resource-efficient hardware such as multi-core workstations and small computer clusters. TURBOMOLE specializes in electronic structure methods with outstanding accuracy–cost ratio, such as density functional theory including local hybrids and the random phase approximation (RPA), GW-Bethe–Salpeter methods, second-order Møller–Plesset theory, and explicitly correlated coupled-cluster methods. TURBOMOLE is based on Gaussian basis sets and has been pivotal for the development of many fast and low-scaling algorithms in the past three decades, such as integral-direct methods, fast multipole methods, the resolution-of-the-identity approximation, imaginary frequency integration, Laplace transform, and pair natural orbital methods. This review focuses on recent additions to TURBOMOLE’s functionality, including excited-state methods, RPA and Green’s function methods, relativistic approaches, high-order molecular properties, solvation effects, and periodic systems. A variety of illustrative applications along with accuracy and timing data are discussed. Moreover, available interfaces to users as well as other software are summarized. TURBOMOLE’s current licensing, distribution, and support model are discussed, and an overview of TURBOMOLE’s development workflow is provided. Challenges such as communication and outreach, software infrastructure, and funding are highlighted.

We present an implementation of pair natural orbital coupled cluster singles and doubles with perturbative triples, PNO-CCSD(T), which avoids the quasi-canonical triples approximation (T0) where couplings due to off-diagonal Fock matrix elements are neglected. A numerical Laplace transformation of the canonical expression for the perturbative (T) triples correction is used to avoid an I/O and storage bottleneck for the triples amplitudes. Results for a test set of reaction energies show that only very few Laplace grid points are needed to obtain converged energy differences and that PNO-CCSD(T) is a more robust approximation than PNO-CCSD(T0) with a reduced mean absolute deviation from canonical CCSD(T) results. We combine the PNO-based (T) triples correction with the explicitly correlated PNO-CCSD(F12*) method and investigate the use of specialized F12-PNOs in the conventional triples correction. We find that no significant additional errors are introduced and that PNO-CCSD(F12*)(T) can be applied in a black box manner.

We present our current progress on the combination of explicit electron correlation with the pair natural orbital (PNO) representation. In particular we show cubic scaling PNO-MP2-F12, and PNO-CCSD[F12] implementations. The PNOs are constructed using a hybrid scheme, where the PNOs are generated in a truncated doubles space, spanned by orbital specific virtuals obtained using an iterative eigenvector algorithm. We demonstrate the performance of our implementation through calculations on a series of glycine chains. The accuracy of the local approximations is assessed using the S66 benchmark set, and we report for the first time explicitly correlated CCSD results for the whole set and improved estimates for the CCSD/CBS limits. For several dimers the PNO-CCSD[F12] calculations are more accurate than the current reference values. Additionally, we present pilot applications of our PNO-CCSD[F12] code to host-guest interactions in a cluster model for zeolite H-ZSM-5 and in a calix[4]arene-water complex.

The measurement of regional lung ventilation by electrical impedance tomography (EIT) has been evaluated in many experimental studies. However, EIT is not routinely used in a clinical setting, which is attributable to the fact that a convenient concept for how to quantify the EIT data is missing. The definition of region of interest (ROI) is an essential point in the data analysis. To date, there are only limited data available on the different approaches to ROI definition to evaluate regional lung ventilation by EIT. For this survey we examined ten patients (mean age +/- SD: 60 +/- 10 years) under controlled ventilation. Regional tidal volumes were quantified as pixel values of inspiratory-to-expiratory impedance differences and four types of ROIs were subsequently applied. The definition of ROI contours was based on the calculation of the pixel values of (1) standard deviation from each pixel set of impedance data and (2) the regression coefficient from linear regression equations between the individual local (pixel) and average (whole scan) impedance signals. Additionally, arbitrary ROIs (four quadrants and four anteroposterior segments of equal height) were used. Our results indicate that both approaches to ROI definition using statistical parameters are suitable when impedance signals with high sensitivity to ventilation-related phenomena are to be analyzed. The definition of the ROI contour as 20-35% of the maximum standard deviation or regression coefficient is recommended. Simple segmental ROIs are less convenient because of the low ventilation-related signal component in the dorsal region.

We study how with means of Gaussian Process Regression (GPR) geometry optimizations, which rely on numerical gradients, can be accelerated. The GPR interpolates a local potential energy surface on which the structure is optimized. It is found to be efficient to combine results on a low computational level (HF or MP2) with the GPR-calculated gradient of the difference between the low level method and the target method, which is a variant of explicitly correlated Coupled Cluster Singles and Doubles with perturbative Triples correction CCSD(F12*)(T) in this study. Overall convergence is achieved if both the potential and the geometry are converged. Compared to numerical gradient-based algorithms, the number of required single point calculations is reduced. Although introducing an error due to the interpolation, the optimized structures are sufficiently close to the minimum of the target level of theory meaning that the reference and predicted minimum only vary energetically in the μE regime.

This work assesses the performance of DLPNO-CCSD­(T0), DLPNO-MP2, and density functional theory methods in calculating the binding energies of a representative test set of 45 atmospheric acid–acid, acid–base, and acid–water dimer clusters. The performance of the approximate methods is compared to high level explicitly correlated CCSD­(F12*)­(T)/complete basis set (CBS) reference calculations. Out of the tested density functionals, ωB97X-D3­(BJ) shows the best performance with a mean deviation of 0.09 kcal/mol and a maximum deviation of 0.83 kcal/mol. The RI-CC2/aug-cc-pV­(T+d)­Z level of theory severely overpredicts the cluster binding energies with a mean deviation of −1.31 kcal/mol and a maximum deviation up to −3.00 kcal/mol. Hence, RI-CC2/aug-cc-pV­(T+d)­Z should not be utilized for studying atmospheric molecular clusters. The DLPNO variants are tested both with and without the inclusion of explicit correlation (F12) in the wavefunction, with different pair natural orbital (PNO) settings (loosePNO, normalPNO, and tightPNO) and using both double and triple zeta basis sets. The performance of the DLPNO-MP2 methods is found to be independent of PNO settings and yield low mean deviations of −0.84 kcal/mol or below. However, DLPNO-MP2 requires explicitly correlated wavefunctions to yield maximum deviations below 1.40 kcal/mol. For obtaining high accuracy, with maximum deviation below ∼1.0 kcal/mol, either DLPNO-CCSD­(T0)/aug-cc-pVTZ (normalPNO) calculations or DLPNO-CCSD­(T0)-F12/cc-pVTZ-F12 (normalPNO) calculations are required. The most accurate level of theory is found to be DLPNO-CCSD­(T0)-F12/cc-pVTZ-F12 using a tightPNO criterion which yields a mean deviation of 0.10 kcal/mol, with a maximum deviation of 0.20 kcal/mol, compared to the CCSD­(F12*)­(T)/CBS reference.

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Electrical impedance tomography (EIT) has the potential to become a new tool for bedside monitoring of regional lung ventilation. The aim of our study was to assess the reproducibility of regional lung ventilation distribution determined by EIT during mechanical ventilation under identical ventilator settings. The experiments were performed on 10 anaesthetized supine pigs ventilated in a volume-controlled mode. EIT measurements were performed with the Goe-MF II device (Viasys Healthcare, Höchberg, Germany) during repeated changes in positive end-expiratory pressure (PEEP) from 0 to 10 cm H2O. Regional lung ventilation was determined in the right and left hemithorax as well as in 64 regions of interest evenly distributed over each chest side in the ventrodorsal direction. Ventilation distributions in both lungs were visualized as ventrodorsal ventilation profiles and shifts in ventilation distribution quantified in terms of centres of ventilation in relation to the chest diameter. The proportion of the right lung on total ventilation in the chest cross-section was 0.54+/-0.04 and remained unaffected by repetitive PEEP changes. Initial PEEP increase resulted in a redistribution of ventilation towards dorsal lung regions with a shift of the centre of ventilation from 45+/-3% to 49+/-3% of the chest diameter in the right and from 47+/-2% to 50+/-2% in the left hemithorax. Excellent reproducibility of the results in the individual regions of interest with almost identical patterns of ventilation distribution was found during repeated PEEP changes.